GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 04:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# On the number line above, p, q, r, s, and t are five consec

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 172
On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

07 Dec 2012, 07:30
36
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:26) correct 18% (01:43) wrong based on 1746 sessions

### HideShow timer Statistics

Attachment:

Number line.png [ 2.33 KiB | Viewed 41579 times ]
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

07 Dec 2012, 07:37
7
6

On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

{p, q, r, s, t} is an evenly spaced set thus its mean = median = middle term = r.

(1) q + s =24. Since q, r and s are consecutive even integers, then q=r-2 and s=r+2 --> (r-2)+(r+2)=24 --> r=12. Sufficient.

(2) The average (arithmetic mean) of q and r is 11. (r-2)+r=2*11 --> r=12. Sufficient.

_________________
##### General Discussion
Intern
Joined: 12 Nov 2012
Posts: 5
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

10 Dec 2012, 07:26
which is the level of the question? 500? tks a lot
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

10 Dec 2012, 07:42
fabrizio1983 wrote:
which is the level of the question? 500? tks a lot

I'd say it's ~600.

P.S. You can see the difficulty level of a question in the first post where the tags are (TAGS: Difficulty: 600-700 Level).
_________________
Intern
Joined: 24 Apr 2012
Posts: 44
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

11 Dec 2012, 03:54
1
Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Ans. : Let p=x, q=x+2, r=x+4 , s=x+6, t=x+8 to find the mean we need to find x.
From statement 1 , we get 2x+8=24
From statement 2 we get x+3=11
Intern
Joined: 06 Dec 2012
Posts: 4
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

16 Dec 2012, 12:38
My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

16 Dec 2012, 22:41
1
1
My understanding of consecutive integers, is that they are separated by only 1, i.e. 3, 4, 5, 6, 7, 8

I was able to find the first statement sufficient, but not the second, mainly because the answer uses the formula p + (p+2) +....

Why is 2 being added to P?

We are not told that p, q, r, s, and t are consecutive integers. We are given that p, q, r, s, and t are five consecutive EVEN integers. For example 2, 4, 6, 8, 10.
_________________
Manager
Joined: 04 Oct 2013
Posts: 155
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

11 Jan 2014, 09:17
They are basically giving us some equation in disguise.

1. q+s=24 but for a fact set we know that the leap between q and s is 4 and this translates into an equation that subtracted gives us the value of q from which we can calculate the average.
2. q+r=22 same old story, the leap between q and r this time is 2 units. r-q=2 subtract it from the given equation and you are done you got one value, the remaining values follow logically.

D.
_________________
learn the rules of the game, then play better than anyone else.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

24 Feb 2015, 21:38
2
1
Hi All,

This DS question is full of Number Properties and the math involved is fairly straight-forward. However, if you don't see the "elegant" approach to answer this question, then you can still use "brute force" and some basic Arithmetic to get the correct answer.

We're given a number line with 5 variables on it. We're told that the variables represent 5 CONSECUTIVE EVEN INTEGERS. That's a very specific set of "restrictions", so you can use them to your advantage if you have to "play around" with this question. We're asked for the AVERAGE of the 5 integers. Since we know that they're consecutive evens, if we can figure out ANY of them, then we can figure out the others AND answer the question.

Fact 1: Q + S = 24

Looking at the drawing, we know that Q, R and S are 3 CONSECUTIVE EVEN INTEGERS, so even if we don't know how to do the Algebra here, we can still run some TESTs....

IF Q, R and S are....
2, 4 and 6, then Q+S = 8. That's too small though (it's supposed to be 24)

IF Q, R and S are a bit bigger, say....
8, 10 and 12, then Q + S = 20. This is still too small, but it's getting closer to 24...

IF Q, R and S are....
10, 12 and 14, then Q + S = 24. This is a MATCH for what we're looking for. We can also figure out the missing values (they're 8 and 16).

By making these variables larger or smaller, the sum of Q+S won't = 24, so we know that the 10/12/14 example is the ONLY possibility that fits.
Fact 1 is SUFFICIENT.

Fact 2: The average of Q and R is 11

Since Q and R are 2 CONSECUTIVE EVEN INTEGERS, we're going to need 2 numbers that are close to 11....

IF Q and R are....
8 and 10, then the average is 9 (which is not a match; it's supposed to be 11)

IF Q and R are...
10 and 12, then the average is 11. This is a MATCH.

Making Q and R any bigger will raise the average (and it won't match), so we know that 10 and 12 are the ONLY possible values that fit. The other numbers would be 8, 14 and 16.
Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)
On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

Updated on: 06 Mar 2020, 06:36
Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Solution:

Recall that in a set of evenly spaced numbers, mean is equal to the median. Thus, the average of these five integers is equal to r.

Statement One Alone:

q + s = 24

Notice that the set consisting of q, r and s is also evenly spaced; therefore the mean of this set is also equal to the median, which is r. Recall that for a set of evenly spaced numbers, the mean is equal to the average of the greatest and the smallest elements; thus r = mean = (q + s)/2 = 24/2 = 12.

Statement one alone is sufficient.

Statement Two Alone:

The average of q and r is 11.

Since (q + r)/2 = 11, q + r = 22. Since q and r are consecutive even integers, q = r - 2. Then, (r - 2) + r = 2r - 2 = 22. Solving the equation, we get r = 12.

Statement two alone is sufficient.

_________________

# Scott Woodbury-Stewart | Founder and CEO | Scott@TargetTestPrep.com

250 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Originally posted by ScottTargetTestPrep on 14 May 2016, 04:56.
Last edited by ScottTargetTestPrep on 06 Mar 2020, 06:36, edited 1 time in total.
Director
Joined: 02 Sep 2016
Posts: 620
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

01 Apr 2017, 09:41
Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24
(2) The average (arithmetic mean) of q and r is 11.

Given:
CONSECUTIVE EVEN INTEGERS
p=2n
q=2n+2
r=2n+4
s=2n+6
t=2n+8

p<q<r<s<t

Mean= (2n+2n+2+2n+4+2n+6+2n+8)/5
= (10n+20)/5
=10(n+2)/5
=2(n+2)

(1) q+s=24
2n+2+2n+6=24
One variable thus can be solved.

Sufficient.

(2) Mean= (2n+2+2n+4)/2

One variable thus can be solved.

D
Intern
Joined: 09 Jan 2017
Posts: 5
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

19 Jul 2017, 08:23
STatement 1 no. of terms is 5 so the center term i.e r will be the avg as the series is an Arithmetic progression
so it can be found by (q +s)/2 = 12.

Statement 2 : given :- (q + r) / 2 = 11.
also q = r-2 (as all are even consecutive integers in a series.)
So again the avg can be found out.

Senior Manager
Joined: 29 Jun 2017
Posts: 411
GPA: 4
WE: Engineering (Transportation)
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

17 Aug 2017, 02:07
1) q+s=24
p,q,r,s,t

s-q= 4 and s+q =24. add them. s=14 and series will be 8,10,12,14,16 and mean will be 12. sufficient A/D can be answer

2) mean of q and r is 11, q+r=22.
r+q=22 , r-q =2 add them r=12, and series will be again same and same answer as above therefore sufficient

Retired Moderator
Joined: 19 Mar 2014
Posts: 904
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

18 Aug 2017, 23:44
2
Attachment:
Number line.png
On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?

(1) q + s =24

As we know that r is the median of q and s, and r is also the median of p,q,r,s, and t. Hence, if we know the value of r we should be able to answer the question.

q + s = 24

Midpoint = 24/2 = 12 = r

Hence, (1) ===== is SUFFICIENT

(2) The average (arithmetic mean) of q and r is 11

q = r - 2

r - 2 + r = 11 * 2

2r = 24

r = 12

Hence, (2) ===== is SUFFICIENT

Did you like the answer? Hit Kudos
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
SVP
Joined: 23 Feb 2015
Posts: 2005
On the number line above, p, q, r, s, and t are five consec  [#permalink]

### Show Tags

Updated on: 06 Mar 2020, 07:52
1
Updated - Thank you for bring it up.
Thanks__

Originally posted by TheUltimateWinner on 04 Mar 2020, 02:50.
Last edited by bb on 06 Mar 2020, 07:52, edited 1 time in total.
Quote removed - thanks for bringing it up
On the number line above, p, q, r, s, and t are five consec   [#permalink] 04 Mar 2020, 02:50